Online research in philosophy

We investigate a variant of the variable convention proposed at Tractatus 5.53ff for the purpose of eliminating the identity sign from logical notation. The variant in question is what Hintikka has called the strongly exclusive interpretation of the variables, and turns out to be what Ramsey initially (and erroneously) took to be Wittgenstein's intended method. We provide a tableau calculus for this identity-free logic, together with soundness and completeness proofs, as well as a proof of mutual interpretability with first-order logic with identity.

Can a person ever occurrently believe p and yet have the simultaneous, occurrent belief q that this very belief that p is false? Surely not, most would say: that description of a person’s epistemic economy seems to misunderstand the very concept of belief. In this paper I question this orthodox assumption. There are, I suggest, cases where we have a first-order mental state m that involves taking the world to be a certain way, yet although we ourselves acknowledge that we are in m, we reflectively disavow m’s propositional content. If such an epistemic stance is possible, does this irrationally persistent first-order state m really deserve the title of belief, or should it instead be classified under some other, less doxastic appellation? I argue in this paper that the belief terminology is warranted, and thus, that we can be correctly described as having the second-order belief that a specific first-order belief that we nonetheless continue to hold is false. In such cases, our first-order state is what I refer to as a naughty belief. Like naughty toddlers, naughty beliefs are recalcitrant in the face of epistemic authority.

This paper proposes a way of semantically representing de re belief ascriptions that involves contextual resolution of the acquaintance relation between the attitude holder and the object about which the attitude is de re. A special case is that where the belief is about the believer herself. Here, we may discern two possibilities: the acquaintance relation is equality, in which case we end up with a de se belief, or, if the first option fails, we search the context for a different suitable relation of acquaintance between the believer and herself, like looking in a mirror or seeing yourself on TV. This second option leaves open the possibility that the believer herself is unaware of the fact that she's actually seeing herself, thereby accounting for the true reading (de re/non-de se) of ``Lain believes she will win'' in mistaken identity scenarios. To implement all this formally, I use a two-dimensionally modal extension of DRT, and second order binding and unification.

Truth and the aim of belief -- Belief, interpretation, and Moore's paradox -- Belief, sensitivity, and safety -- Basic beliefs and the problem of non-doxastic justification -- Experience as reason for beliefs -- The problem of the basing relation -- Basic beliefs, easy knowledge, and the problem of warrant transfer -- Belief, justification, and fallibility -- Knowledge of our beliefs and privileged access.

ABSOLUTE AND RELATIVE IDENTITY On the classical, or Fregean, view of identity it is an equivalence relation satisfying Leibniz's Law (so<alled), ...

A widely accepted view in the discussion of personal identity is that the notion of psychological continuity expresses a one–many or many–one relation. This belief is unfounded. A notion of psychological continuity expresses a one–many or many–one relation only if it includes, as a constituent, psychological properties whose relation with their bearers is one–many or many–one; but the relation between an indexical psychological state and its bearer when first tokened is not a one–many or many–one relation. It follows that not all types of psychological continuity may take a one–many or many–one form. This conclusion casts doubt on the Lockean approach to the issue, by showing that the notion of psychological continuity Lockeans rely on may not be available.

Pure second-order logic is second-order logic without functional or first-order variables. In "Pure Second-Order Logic," Denyer shows that pure second-order logic is compact and that its notion of logical truth is decidable. However, his argument does not extend to pure second-order logic with second-order identity. We give a more general argument, based on elimination of quantifiers, which shows that any formula of pure second-order logic with second-order identity is equivalent to a member of a circumscribed class of formulas. As a corollary, pure second-order logic with second-order identity is compact, its notion of logical truth is decidable, and it satisfies a pure second-order analogue of model completeness. We end by mentioning an extension to n th-order pure logics.

The AGM (Alchourrón-GÄrdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that arenot closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that onefirst adds the new belief to the belief base, and afterwards contracts its negation. It is argued that external revision represents an intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief.

We show how some model-theoretical devices (local reasoning, modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize the consequence relation that includes de dicto and de re contradictory beliefs. Instead of special ``sense objects'', appearances of objects in an agent's belief are introduced and presented as ordered pairs consisting of an object and an individual constant. A non-classical identity relation is applied. A relation S on the set of possible worlds is introduced, which models possible distortions in an agent's picture of a (real) world. The application of such models in deontic logic is illustrated by a characteristic example. , , , , , , , ,.

On the ground of Kant’s reformulation of the principle of con- tradiction, a non-classical logic KC and its extension KC+ are constructed. In KC and KC+, \neg(\phi \wedge \neg\phi),  \phi \rightarrow (\neg\phi \rightarrow \phi), and  \phi \vee \neg\phi are not valid due to specific changes in the meaning of connectives and quantifiers, although there is the explosion of derivable consequences from {\phi, ¬\phi} (the deduc- tion theorem lacking). KC and KC+ are interpreted as fragments of an S5-based first-order modal logic M. The quantification in M is combined with a “subject abstraction” device, which excepts predicate letters from the scope of modal operators. Derivability is defined by an appropriate labelled tableau system rules. Informally, KC is mainly ontologically motivated (in contrast, for example, to Jaśkowski’s discussive logic), relativizing state of affairs with respect to conditions such as time.