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Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility...
The main ideas behind Brouwer’s philosophy of Intuitionism are presented. Then some critical remarks against Intuitionism made by William Tait in “Against Intuitionism” [Journal of Philosophical Logic, 12, 173–195] are answered.
Knowledge-based programs (KBPs) are a powerful notion for expressing action policies in which branching conditions refer to implicit knowledge and call for a deliberation task at execution time. However, branching conditions in KBPs cannot refer to possibly erroneous beliefs or to graded belief, such as “if my belief that φ holds is high then do some action α else perform some sensing action β”. The...
A transformative decision rule alters the representation of a decision problem, either by changing the set of alternative acts or the set of states of the world taken into consideration, or by modifying the probability or value assignments. A set of transformative decision rules is order-independent in case the order in which the rules are applied is irrelevant. The main result of this paper is an...
In ‘belief revision’ a theory $${\cal K}$$ is revised with a formula φ resulting in a revised theory $${\cal K}\ast\varphi$$ . Typically, $$\neg\varphi$$ is in $${\cal K}$$ , one has to give up belief in $$\neg\varphi$$ by a process of retraction, and φ is in $${\cal K}\ast\varphi$$ . We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically...
We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete axiomatization of the qualitative part of Bayes’ rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows and iterated revision are also discussed.
In this paper, a pragmatic approach to the phenomenon of free choice permission is proposed. Free choice permission is explained as due to taking the speaker (i) to obey certain Gricean maxims of conversation and (ii) to be competent on the deontic options, i.e. to know the valid obligations and permissions. The approach differs from other pragmatic approaches to free choice permission in giving a...
* The conference was organized by Giacomo Bonanno, Wiebe van der Hoek, Pierfrancesco La Mura and Arnis Vilks with the assistance of a program committee consisting of Johan van Benthem, Vincent Hendricks, Wlodek Rabinowicz, Hans Rott and Marciano Siniscalchi.
Case studies in the psychophysics, modeling and localization of human vision are presented as an example of “hands-on” philosophy of the cognitive sciences. These studies also yield important results for familiar problems in philosophy of mind: the explanatory gap surrounding phenomenological feels is not closed by the kinds of investigations surveyed. However, the science is able to explain some...
Keeley has recently argued that the philosophical issue of how to analyse the concept of a sense can usefully be addressed by considering how scientists, and more specifically neuroethologists, classify the senses. After briefly outlining his proposal, which is based on the application of an ordered set of individually necessary and jointly sufficient conditions for modality differentiation, I argue,...
The reason why, since Descartes, nobody has found a solution to the mind–body problem seems to be that the problem itself is a false or pseudo-problem. The discussion has proceeded within a pre-Cartesian conceptual framework which itself is a source of the difficulty. Dualism and all its alternatives have preserved the same pre-Cartesian conceptual framework even while denying Descartes’ dualism....
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